Card Magic

Johanna knows mind reading magic, or so she says. Her new
trick consists of lining up $N$ decks of cards, each deck having
$K$ cards numbered from
$1$ to $K$. She asks you to think of a number
$T$ between $1$ and $N \cdot K$ and to focus your thoughts
on it. Then, by scanning the energy profiles emitted from your
brain activity, she carefully picks one card from each of the
$N$ decks. Magically, the
sum of the numbers on the $N$ picked cards is exactly the number
that you were thinking of! After staring at her in disbelief
for quite a while, you suspect it might be a trick she pulls on
many people, and that she just picks the cards at random and
happened to get it right with you just by chance.

You start wondering just how large that chance was. You
could easily compute the number of ways to pick one card from
each deck, but how many of these ways have the correct sum?

Input

The first line contains three space-separated integers
$1 \le N \le 100$,
$1 \le K \le 50$,
$1 \le T \le N \cdot K$ –
the number of decks, the number of cards in each deck, and the
number you were thinking of, respectively.

Output

Output a single integer – the number of ways Johanna could
have picked a card from each deck, such that the picked cards
sum up to $T$. Since this
number can be very large, output it modulo $1\, 000\, 000\, 009$.